Answer:
See Below.
Step-by-step explanation:
Square roots deal with multiplication, so if you can simplify to an even square, you can pull out the integer.
sqrt(75) = sqrt(25×3) = sqrt(25)×sqrt(3) = 5×sqrt(3)
((50 is 25×2, so same 5, but with sqrt(2), not 3))
So...
5 / (5×sqrt(3) - 5×sqrt(2)) = 5 / (5×(sqrt(3) - sqrt(2)))
5's cancel out
1 / (sqrt(3) - sqrt(2))
If you multiply top and bottom by (sqrt(3) + sqrt(2)) (which doesn't technically alter anything, since anything over itself is just 1), you get...
(sqrt(3) + sqrt(2)) / ((sqrt(3))^2 - (sqrt(2))^2 + (sqrt(3)×sqrt(2)) - (sqrt(2)×sqrt(3)))
Which simplifies to...
(sqrt(3) + sqrt(2)) / (3 - 2) = (sqrt(3) + sqrt(2)) / 1 = sqrt(3) + sqrt(2)
